Connectivity-Dependent Conductance of 2,2′-Bipyridine-Based Metal Complexes

The present work provides an insight into the effect of connectivity isomerization of metal-2,2′-bipyridine complexes. For that purpose, two new 2,2′-bipyridine (bpy) ligand systems, 4,4′-bis(4-(methylthio)phenyl)-2,2′-bipyridine (Lmeta) and 5,5′-bis(3,3-dimethyl-2,3-dihydrobenzothiophen-5-yl)-2,2′-bipyridine (Lpara) were synthesized and coordinated to rhenium and manganese to obtain the corresponding complexes MnLmeta(CO)3Br, ReLmeta(CO)3Br, MnLpara(CO)3Br, MoLpara(CO)4 and ReLpara(CO)3Br. The experimental and theoretical results revealed that coordination to the para system, i.e., the metal ion peripheral to the conductance path, gave a slightly increased conductance compared to the free ligand attributed to the reduced highest occupied molecular orbital (HOMO)–least unoccupied molecular orbital (LUMO) gap. The meta-based system formed a destructive quantum interference feature that reduced the conductance of a S···S contacted junction to below 10–5.5Go, reinforcing the importance of contact group connectivity for molecular wire conductance.


S2. Crystallographic data
The X-ray single crystal data have been collected using λMoKα radiation (λ =0.71073Å) on Bruker

Frontier Orbital comparison
Due to the complexity of modelling a rhenium complexes (Re meta and Re para ) in a molecular junction the comparison was made using analogous manganese complexes (Mn meta and Mn para ) shown in figures S18 and S19 are a comparison of the orbital distributions and energies of the rhenium and manganese complexes in the gas phase.The DFT calculations were performed on Gaussian09 5 using B3LYP, for the manganese complexes a 6-31G(d) basis set was employed for all atoms while for the rhenium complexes a 6-31G(d)/LANL2DZ basis was used.In each case the relative atomic contributions to the frontier orbitals we very similar, with the HOMO localised to the metal centre and the LUMO to the ligand (L meta or L para ).There were modest differences observed for the energy levels of the LUMOs, however, the HOMO energies displayed only a negligible difference between the rhenium complexes and their manganese analogues.Taking these factors into account it is reasonable say that the more advanced calculations on the manganese complexes will offer insight into the behaviour of the rhenium complexes.As highlighted in the conductance section, the dominant conductance feature of L meta corresponds to the junction where the pyridyl ring and thiomethyl contact the gold electrode (see Figure S18), denotate as L meta 2 orientation.

Proposed shorter molecules
To compensate for the low conductance of the compounds measured in this paper we propose an analogous series of compounds (see Figure S27) where the anchor groups are directly attached to the pyridyl rings.Shown in Figure S28 are their theoretical conductance values, each showing increased conductance to their longer analogues.This is an important consideration for the development of related systems.molecules L meta-s , L para-s , Mn meta-s and Mn para-s .

Computational Methods
DFT Calculation -The geometry of each structure studied in this paper was relaxed to the force tolerance of 10 meV/Å using the SIESTA 6 implementation of DFT, with a double-ζ polarized basis set (DZP) and the Generalized Gradient Approximation (GGA) functional with Perdew-Burke-Ernzerhof (PBE) parametrization.A real-space grid was defined with an equivalent energy cutoff of 250 Ry.We then calculate spin polarized molecular orbitals and spin density of gas phase molecules.
Spin Transport -To calculate the electronic properties of the device, from the converged DFT calculation, the underlying spin polarized mean-field Hamiltonian Hσ was obtained where σ = ↑, ↓ and ↑ (↓) denotes majority (minority) spin.Hσ was combined with our quantum transport code, GOLLUM 7 .This yields the spin-dependent transmission coefficient Electrical Conductance -Using the approach explained in ref 8 , the electrical conductance is calculated from Landaure's formula =0∫+∞−∞()(−∂(,,F)/∂), where =((−F)/B+1)−1 f is the Fermi-Dirac probability distribution function, T is the temperature, EF is the Fermi energy, G0 = 2e2/h is the conductance quantum, e is the electron charge, and h is the Planck's constant.

Figure S18 .
Figure S18.Frontier orbital comparison between Mn meta and Re meta .

Figure S19 .
Figure S19.Frontier orbital comparison between Mn para and Re para .

Figure S20 .
Figure S20.Structure of molecules between two gold electrodes contacting via the thiomethyl groups.(a) L meta , (b) L para , (c) Mn meta and (d) Mn para .

Figure S28 .
Figure S28.DFT calculated room-temperature electrical conductance for the shortened Tσ(E) for electrons of energy E (passing from the source to the drain) via the relation Tσ(E) = (ΓL()R()ΓR()R †()) where ΓL,R()=(∑L,R() −∑L,R †()) describes the level broadening due to the coupling between left L and right R electrodes and the central scattering region, ΣL,Rσ(E) are the retarded self-energies associated with this coupling and R=(−−∑L −∑R)−1 is the retarded Green's function, where Hσ is the Hamiltonian and S is the overlap matrix obtained from SIESTA implementation of DFT.The total transmission is then calculated from T(E) = (T↑ + T↓)/2.
3and SHELXTL 4 software.All non-hydrogen atoms were refined in anisotropic approximation, hydrogen atoms in structure L Meta were refined

Table S1 .
Crystal data and structure refinement for structures L meta , L para and Re meta .

Table S2 .
Crystal data and structure refinement for structures Re para and Mn meta .